Question

Your financial planner offers you two different investment plans. Plan X is a $22,000 annual perpetuity. Plan Y is an annuity lasting 19 years and an annual payment, $32,000. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans?

Answer 1

At 6.31 % discount rate would you be indifferent between these two plans.

Step-by-step explanation:

given data

plan x = $22,000

plan y = $32,000

time t = 19 year

solution

we will equate here both present value and that is express as

Present Value of Perpetuity =
`(P)/(r)` .................1

Present Value of Annuity =
`(P)/(r)(1 - (1 + r)^(-t))` .............2

equating both equation 1 and 2

`(P)/(r)` =
`(P)/(r)(1 - (1 + r)^(-t))`

\frac{22000}{r} = \frac{32000}{r}(1 - (1 + r)^{-19})

(1 + r)^{-19} = 1 - \frac{22000}{32000}

solve it we get rate r

r = 0.063131

rate = 6.31 %

so at 6.31 % discount rate would you be indifferent between these two plans.